Taking over islands

Peaceful purchase is not in the conquest guide. The handshake icon on the left opens diplomacy. Pick the owner, open negotiations, and choose the war option. After the island is yours, it does not run until a new kontor, the trading post, is built.

“How many hours to take another island” has no measured answer in that article or in the patch notes. It depends on the fleet you already own and on what is defending the coast. I will not print a number of hours.

Update 3.0 fixed a case where, after you had submitted an ally as consul, your units could not attack pirate buildings and the game reported an invalid target. The note says affected saves are included. That bug is about pirates after a consul submission, not about the war declaration itself.